Applicable Analysis and Discrete Mathematics, issue 00, pages 20
Series expansions for powers of sinc function and closed-form expressions for specific partial bell polynomials
Qi Feng
1
,
Peter Taylor
2
1
School of Mathematics and Informatics, Henan Polytechnic University, Jiaozuo, Henan, China + School of Mathematics and Physics, Hulunbuir University, Inner Mongolia, China + Independent researcher, Dallas, USA
|
2
Independent Researcher, Valencia, Spain
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Publication type: Journal Article
Publication date: 2023-10-09
scimago Q2
SJR: 0.483
CiteScore: 2.4
Impact factor: 1
ISSN: 14528630, 2406100X
Applied Mathematics
Discrete Mathematics and Combinatorics
Analysis
Abstract
In the paper, with the aid of the Fa? di Bruno formula, in terms of the central factorial numbers and the Stirling numbers of the second kinds, the authors derive several series expansions for any positive integer powers of the sinc and sinhc functions, discover several closed-form expressions for partial Bell polynomials of all derivatives of the sinc function, establish several series expansions for any real powers of the sinc and sinhc functions, and present several identities for central factorial numbers of the second kind and for the Stirling numbers of the second kind.
Found
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